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Inverse Proportion

Maths: Edexcel A Level Pure Maths, topic 2.5.10

Inverse Proportion

Two variables are inversely proportional to one another if the size of one variable decreases when the size of other increases.

Inversely proportional

Inversely proportional

  • If two numbers are inversely proportional, we write:
  • x∝1yx \large \propto \frac{1}{y}
  • We can always write the equation:
  • x=kyx = \frac{k}{y}
  • Where kk is the constant of proportionality and is a non-zero number.
Example

Example

  • 3 builders take 12 days to build a wall. How long does it take 4 builders to build an identical wall?
  • We expect the time taken to build the wall to decrease as the number of builders increase.
  • This means the time taken and the number of builders are inversely proportional.
Days taken are inversely proportional to builders

Days taken are inversely proportional to builders

  • d = number of days taken
  • b = number of builders
Convert to equation

Convert to equation

It takes 3 builders 12 days to build the wall

It takes 3 builders 12 days to build the wall

Rearrange to find k

Rearrange to find k

Sub k back into the original equation

Sub k back into the original equation

Sub in b 4

Sub in b = 4

  • We want to know the days taken for 4 builders to build the wall.
It takes them 9 days

It takes them 9 days

Test yourself on Inverse Proportion

  • Which of the following means 'x is inversely proportional to y'?

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